Weird deformation with fingers (automatic weights)
The rigging is bad: Select the armature, shift select the object, switch to Weight Paint mode, then select each bone, you’ll see what part of the mesh they affect. You can see that the first thumb phalanx affects the palm, which is not supposed to do. Some other phalanx also affect the palm.



So you need to:


Create a bone for the palm itself
Parent this bone to the last arm bone (Keep Offset mode).
Parent each first phalanx to this bone (Keep Offset mode).





In Weight Paint mode, paint the influence of the palm bone (enable the 2D Falloff option to paint through the mesh).





Also remove all the unnecessary influences.




Now it works fine (don't know why your arm has 3 bones though).